The CLIO system was used to measure the impulse response
of each individual driver, mounted in a test panel. Here I will use the impulse
response for the tweeter/midrange combination (17.9 kb) as an example. The
starting point for the time sample (or time-gate) used to derive the frequency
response establishes the phase reference point. The reference point can be moved
back and forth until the phase pattern is nearly
flat (25.4 kb) vs. frequency. In the example the starting time, shown on
the right-hand side of the CLIO window, is 3.85 milliseconds. Sound travels
1.32 meters in this time interval, so the phase reference is 1.32 meters in
front of the calibrated microphone. By measuring the distance from the mike
to the driver, the point is then determined relative to the driver. The reference
point location for a flat phase pattern is shown for each of the three drivers
as the red circles in the illustration on time-alignment
(5.5 kb). With respect to these reference points, all three drivers have nearly
equal phase patterns within their respective frequency bands. Therefore, with
the reference points aligned on the same vertical plane, the sound from the
three drivers will combine with near-perfect coherence in the forward direction.
That was the technique used to determine the terracing dimensions. (Strictly
speaking, I suppose this should be called phase-alignment, but the result is
equivalent to time-alignment).

It is odd that the reference points are in front
of the tweeter and midrange. Stefanos Albanidis has kindly shared measurements
that he made on a similar tweeter using a later version of CLIO. His measurement
shows the reference point is 1.4 cm behind the faceplate. He also stated that
my version of the CLIO system may be measuring this incorrectly. As far as my
speaker design is concerned, I only need to accurately know the relative distance
between the points for the three drivers. This is correct as evidenced by the
combined measurements of the drivers, even if the absolute location of the points
are shifted.

Note added 3/19/98. Audiomatica kindly gave me a
CLIO upgrade from v3.2 to v4.0. When I repeated the time-alignment measurement,
this time the origin was right at the tweeter face-plate.

The correct geometrical alignment of the drivers
is not sufficient to guarantee good time-alignment. The crossover design is
also critical. This is discussed in detail in the section
on system design. The example phase pattern for the tweeter and midrange
includes the crossover, and shows that true time-alignment was achieved for
the total system response.

The time alignment is perfectly accurate only at
a height midway between the midrange and tweeter. (The woofer has relatively
little effect on time-alignment). The geometry is designed so this height is
at ear-level in the "sweet spot" where I sit. If I stand up instead of sitting,
the path-lengths from the tweeter and midrange to my ears are no longer equal.
For the geometry of my enclosure and room (7.2
kb), the difference in pathlength in this case is 1.13 inches. At a the crossover
frequency of 3000 Hz, the sound from the tweeter and midrange will have a relative
phase shift of 90 degrees due to this pathlength difference. However this is
just part of the story. The 1st order crossover introduces a 90 degree phase
shift also, and the net result is that the midrange and tweeter are 180 degrees
out of phase at this point.

I computed the sound
pressure (12 kb) along the vertical path 140 inches from the reference points
shown in the geometry illustration, for 10 frequencies. The horizontal axis
in these Figures is the response in dB; the vertical axis for the left-hand
Figure is the vertical movement in inches above the point between the midrange
and tweeter. The numerals adjacent to some of the curves are the frequency in
kHz for the curve. For my system, the left-hand Figure, the 3 kHz curve has
a null 19 inches above the midpoint as expected (this corresponds to the 23"
dimension in the geometry illustration).

A D'Appolito array straddles the tweeter with two
midrange drivers. This creates a virtual phase reference point in between the
two midrange speakers, and eliminates lobing between the midrange and tweeter.
However it creates new lobing between the two midrange speakers. These drivers
are twice as far apart as the midrange and tweeter. However, with the same crossover
the variation is less than with a single midrange, as shown in the right-hand
Figure. For the D'Appolito Figure the vertical offset is relative to the tweeter.
Since the phase shift introduced by the crossover is an important part of this
behavior, these curves apply only to 1st order crossovers. I have not made any
calculations for other orders.

Lobing is a fairly complicated phenomenon, and the
calculations do not include the drop-off in driver response as the angle off
axis increases. I measured the response of my system
(46 kb) and the null for a vertical offset of 19 inches was there just as predicted
(ain't engineering wonderful). The red curve is measured at the sweet spot,
and the yellow curve at the elevated position.

The vertical size of the "sweet spot" is increased
by decreasing the vertical spacing between the tweeter and midrange, so I put
them as close as I could without creating a diffraction problem. For my purposes
the "sweet spot" is large enough that lobing is not a problem. But I must say,
after starting out very skeptical about the D'Appolito configuration, I have
been converted into a believer. For an application where the "sweet spot" needs
to be large vertically, it is clearly a superior arrangement with a 1st order
crossover.

Shortly after writing this sentence, it finally occurred
to me to calculate the response moving below the sweet spot. Normally,
of course, the lowest my ear will be is when I am sitting down, which is why
I didn't do this calculation the first time around. The D'Appolito array is
symmetrical with respect to movement up or down, and the result for it is a
flipped version of the graph already shown. However for the single midrange
and tweeter, the situation is not symmetrical, because of the phase shift introduced
by the crossover. The resulting curve for a downward
movement (8.5 kb) shows a much broader sweet spot, and if anything it is
a little better than the D'Appolito array. If I had made this calculation a
few months ago, I probably would have built the speakers with the midrange above
the tweeter. I think every speaker I have ever seen has the tweeter on top,
and I just blindly followed tradition. It also did not occur to me that the
crossover phase shift would introduce and asymmetry, until I actually did the
calculations shown here. Oh well, live and learn.